ajaz_eco_204_2012_2013_chapter_11_producer_theory_PP

Eco 204 s ajaz hussain do not distribute thus holding

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Unformatted text preview: 204, S. Ajaz Hussain. Do not distribute. Thus, holding all other inputs constant, the “sub” production function for sweeteners is: As such, the production function becomes: ( ) ( ) (f) For the production function in part (e), calculate the optimal inputs and cost function of producing target output . Show all calculations below. Answer At the optimum, to produce target output it must be that: ( ) This implies: Notice there are 5 unknowns ( as: ) but only 4 equations. To handle such an equation, express the cost function () () We know that: 21 ECO 204 Chapter 11: Practice Problems & Solutions for Producer Theory – The Basics in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. The cost function becomes: () () ( ) () () ( ) ( ) This is a linear function with 1 unknown, sugar ( ). The intercept is ( ). If the cost function becomes: ) The slope is ( C(q) (PF + PL+ PK + PM) q Sugar In this case, the optimal amount of sugar is zero. This makes sense because sugar and fructose are perfect substitutes, where a unit of sugar is the same as 2 units of fructose (i.e. the “sweetener” iso-quant has slope -2). If the “cost function” is steeper than the iso-quant, then we should use no sugar. This happens when: 22 ECO 204 Chapter 11: Practice Problems & Solutions for Producer Theory – The Basics in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Therefore, if the optimal inputs are: () The cost function becomes: () () ( ) ( )( ) () On the other hand, if ( ) ( ( ) ) Ajax will use only sugar as a sweetener: The cost function becomes: () () ( ) ( ( )( ) () ) ( ) ( () ( ) ) 23 ECO 204 Chapter 11: Practice Problems & Solutions for Producer Theory – The Basics in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (g) What is the elasticity of total cost with respect to sugar prices in the “new” technology? Was it a good idea for Ajax Cola to have reconfigured its technology to allow the use of sugar and/or fructose as sweeteners? Show all calculations below. Answer The answer depends on whether When or . the cost function is: () ( ) () ( ) In this case: When the cost function is: In this case: ( ( ) ) Notice that when sugar is too expensive (i.e. ) the elasticity with the new technology is 0, lower than the elasticity with the old technology. When , the elasticity is less than what it was before, i.e. cost is less sensitive to sugar price movements. Thus, the new technology is better because when sugar price are too high, Ajax can substitute fructose for sugar. (h) Suppose 0.25. What is the expected cost of producing and with probability 0.75 and units? Show all calculations below. with probability Answer The expected price of sugar is: ( ) ( ) 24 ECO 204 Chapter 11: Practice Problems & Solutions for Producer Theory – The Basics in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Which cost function we use depends on whether . In this case, the relevant cost function is: () ( Note that ( () or so that ) )( ) () 25 ECO 204 Chapter 11: Practice Problems & Solutions for Producer Theory – The Basics in ECO 204 (this version 2012-2013)...
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